Shown in the figure is a hollow ice-cream cone (it is open at top). If its mass is $M$ , radius of its top is $R$ and height, $H$ , then its moment of inertia about its axis is

Question

Shown in the figure is a hollow ice-cream cone (it is open at top). If its mass is M , radius of its top is R and height, H , then its moment of inertia about its axis is

TestHub · Accepted Answer

It can be assumed as several parts of discs having different radius, so

$I = \int dl = \int dm (r^{2})$

From diagram

$\frac{r}{y} = \tan θ = \frac{R}{H}$

$r = \frac{R}{H} \cdot y$

$dm = ρ (π r^{2}) dy$

From equation (i), (ii) and (iii)

$I = \frac{M R^{2}}{2}$

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